2018 Annual Reliability and Maintainability Symposium (RAMS 2018)

1 / 2017-04-16 13:13:07

Contemporaneous Failure Time Analysis Using Poisson Probability

13490,1801,13489

A method of repairable equipment failure time analysis using Poisson probability values (p-value) is described and illustrated. Failures of interest are those that do not conform to the Poisson distribution formed by the database; therefore, the Poisson distribution is used in reverse to identify non-conforming failures. The Poisson is a null hypothesis. The p-values provide statistical evidence for the failure being special cause or common cause.
The data can be analyzed contemporaneously as the failure data are generated. This immediate analysis of the incoming failure data provides timely indication of reliability change. P-values for the last failure time as well as p-values for the sum of the last time plus any number of immediately prior failure events are used in making a decision to investigate the failure or not. The probability levels that trigger investigation can be adjusted for asset criticality, available investigation resources and tolerance for false positives. An immediate investigation provides the opportunity to intervene in reliability deterioration and thereby avoid future failures.
The probability values indicate the likelihood that random variation alone can account for the time of the events; therefore, they also measure the likelihood of a false positive. A false positive is one in which failure is investigated because of suspected special cause, but failure time is actually driven by random variation, i.e., it is a common cause failure. The Poisson p-value complement is the probability of special cause failure worthy of investigation.
A trend of failure count cumulative residuals from the count predicted by the dataset mean provides a sensitive visualization of the data for selecting data for probability analysis. The trend graph can also be linked to the Poisson probability calculations. The trend and analysis method are demonstrated with a dataset that is frequently used in the reliability literature. A probability map for the dataset with 10 Poisson p-values for each failure time is developed to visually illustrate the increasing evidence for intervention in this classic example.
With contemporaneous analysis, datasets can sometimes be quite small. If the true MTBF were known, small datasets would be no problem. But the true MTBF needed for the Poisson distribution is unknown. Our experienced failure times are only samples drawn from the unknown true MTBF. The average of these failure times is only an estimate of the true MTBF. The volatility and subsequent stabilization of MTBF with increasing failure counts is demonstrated with Monte Carlo simulation. With this consideration, distributions for the Poisson p-values in the probability map were formed. With only two failures for example, Poisson probabilities should be considered to be conditional, that is, conditional on the MTBF used in the distribution. The conditional requirement can be with lifted with only few additional failures.